Subgroups — #13123214

Order 1664.

504 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88123	C₂	1	2	yes	maximal
2	C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic
3	#11718597	C₂	1	4	yes	maximal
4	#11718590	C₂	1	8	yes	maximal
5	C₂²×Dic₂₆	C₂²	1	4	yes	—
6	C₂×C₄²×C₁₃	C₂²	1	4	yes	—
7	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₁₃	C₂²	1	4	yes	—
10	C₂×C₄⋊Dic₁₃	C₂²	1	4	yes	—
11	#88123	—	2	8	no	—
12	#88071	C₂²	1	16	yes	—
13	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
14	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
15	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
16	C₂²×Dic₁₃	C₂³	1	8	yes	—
17	C₂×Dic₂₆	—	2	8	no	—
18	C₂×Dic₂₆	—	2	16	no	—
19	C₄²×C₁₃	—	2	8	no	—
20	C₄²×C₁₃	D₄	1	4	yes	—
21	C₄²×C₁₃	Q₈	1	8	yes	complemented
22	C₄⋊Dic₁₃	—	2	8	no	—
23	C₄⋊Dic₁₃	—	2	8	no	—
24	#2862	—	13	1	no	maximal, Sylow
25	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
26	C₂×C₄×C₁₃	—	2	8	no	—
27	C₂×C₄×C₁₃	C₂×D₄	1	4	yes	—
28	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
29	C₂×C₄×C₁₃	C₂×Q₈	1	8	yes	—
30	C₂×C₄×C₁₃	C₂×Q₈	1	4	yes	—
31	C₂×C₄×C₁₃	#41	1	8	yes	—
32	C₂×Dic₁₃	—	2	8	no	—
33	C₂×Dic₁₃	—	2	16	no	—
34	Dic₂₆	—	4	16	no	—
35	C₂×C₄⋊Q₈	—	13	2	no	—
36	#391	—	13	8	no	—
37	#382	—	13	4	no	—
38	C₄³	D₁₃	1	1	yes	characteristic
39	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
40	C₂²×C₁₃	C₂²×Q₈	1	2	yes	—
41	C₂²×C₁₃	C₂×#41	1	4	yes	—
42	C₄×C₁₃	—	2	8	no	—
43	C₄×C₁₃	#124	1	8	yes	—
44	C₄×C₁₃	C₄⋊Q₈	1	4	yes	—
45	Dic₁₃	—	4	8	no	—
46	C₂²×Q₈	—	13	4	no	—
47	C₄⋊Q₈	—	26	8	no	—
48	C₂×C₄⋊C₄	—	13	4	no	—
49	C₂×C₄⋊C₄	—	13	4	no	—
50	C₂×C₄²	C₂×D₁₃	1	4	yes	—
51	C₂×C₄²	C₂×D₁₃	1	2	yes	—
52	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
53	#95	—	13	16	no	—
54	C₂×C₁₃	C₂×#124	1	2	yes	—
55	C₂×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
56	C₂×C₁₃	#533	1	4	yes	—
57	C₂×Q₈	—	26	8	no	—
58	C₂×Q₈	—	26	16	no	—
59	C₂²×C₄	—	13	8	no	—
60	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
61	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
62	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
63	C₄⋊C₄	—	26	8	no	—
64	C₄⋊C₄	—	26	8	no	—
65	C₄²	—	2	8	no	—
66	C₄²	Dic₂₆	1	8	yes	complemented
67	C₄²	D₅₂	1	4	yes	—
68	C₁₃	#2862	1	1	yes	characteristic, complemented, Sylow
69	C₂³	C₂³×D₁₃	1	1	yes	characteristic
70	Q₈	—	52	16	no	—
71	C₂×C₄	—	2	8	no	—
72	C₂×C₄	—	26	8	no	—
73	C₂×C₄	—	26	16	no	—
74	C₂×C₄	C₂×Dic₂₆	1	8	yes	—
75	C₂×C₄	C₂×Dic₂₆	1	4	yes	—
76	C₂×C₄	C₂×D₅₂	1	2	yes	—
77	C₂×C₄	C₂×D₅₂	1	4	yes	—
78	C₂×C₄	#6127	1	8	yes	—
79	C₂²	C₂²×Dic₂₆	1	2	yes	—
80	C₂²	C₂²×D₅₂	1	1	yes	characteristic
81	C₂²	C₂×#6127	1	4	yes	—
82	C₄	—	2	8	no	—
83	C₄	—	52	8	no	—
84	C₄	#88123	1	4	yes	—
85	C₄	#88129	1	8	yes	—
86	C₂	C₂×#88123	1	1	yes	characteristic
87	C₂	#11719175	1	4	yes	—
88	C₂	C₂×#88129	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃
commutator, socle, prime radical, cosocle	C₂³×C₁₃	C₂⁴
Fitting	C₄³×C₁₃	C₂
hypercenter	C₄³	D₁₃
hypocenter	C₁₃	#2862
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₄³

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
21. C₄²×C₁₃	Q₈	semidirect
66. C₄²	Dic₂₆	semidirect
68. C₁₃	#2862	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#88123	2
C₄³×C₁₃	2
#11718597	2
#11718590	2
#2862	13